Workpiece supports are used to support workpieces, for example, in a laser cutting machine. The workpiece supports that are loaded with the workpieces are conveyed by means of a transport device toward and away from the processing machine. The workpiece supports form a support plane for supporting the workpieces by means of a plurality of support strips that are spaced from each other and on which the workpieces are located in a discontinuous manner. As a result of the workpiece processing, in particular, the thermal processing of the workpieces, contamination, which impairs the operation of the workpiece support, can become deposited on the support strips. It is also conceivable that a plurality of layers of small workpiece parts, in particular, small sheet metal parts, become baked onto the support strips. The support strips can further become deformed in an undesirable manner owing to thermal and mechanical stresses during operation. Therefore, the workpiece supports are checked, maintained, and cleaned at given time intervals.